# prove pr(E)=0

• September 19th 2010, 11:35 AM
nikie1o2
prove pr(E)=0
Let U be a well defined universe; S be a well defined sample space. Let E= empty set.

Prove or disprove that Pr(E)=0
• September 19th 2010, 04:50 PM
Plato
In the axioms of probability there are at most three axioms.
If $S$ is the space then $P(S)=1$.
If $A\cap B=\emptyset$ then $P(A\cup B)=P(A)+P(B)$.
Using those two it is easy to show that $P(\emptyset)=0$
• September 19th 2010, 11:33 PM
Moo
• September 20th 2010, 01:31 PM
matheagle
note that probability zero doesn't mean the set is empty
For example, the cubs have zero chance of ever winning a world series
and yet they may in 10,000 years